Power limit on mains.

Hi.
Sometimes it happens that if you have a lightbulb and something else that is rated high wattage in the same mains outlet (sometimes even on different outlets), and turn the high-wattage appliance, you can see how the lightbulb gets dimmer.
Why does this happens?

It happens because of voltage drop in the wires/connections. Since no conductor is perfect some voltage is lost when high(er) currents are being carried by said conductors due to their resistance. Ohms law and all...